Kinetic energy formula

The kinetic energy formula, represented as KE = ½ × m v2, establishes a relationship between the kinetic energy (KE) of an object, its mass (m), and the square of its velocity (v). By utilizing this formula, one can calculate the amount of kinetic energy possessed by an object based on its mass and the square of its velocity.

Contents

Practice problems

Problem #1

Calculate the kinetic energy of a ball with a mass of 3 kg and a velocity of 6 m/s.

Solution

Given data:

• Kinetic energy of a ball, KE = ?
• Mass of a ball, m = 3 kg
• Velocity of a ball, v = 6 m/s

Applying the formula:

• KE = ½ × m v2
• KE = ½ × 3 × (6)2
• KE = ½ × 3 × 36
• KE = 54 J

Therefore, the kinetic energy of a ball is 54 J.

Problem #2

What is the kinetic energy of a 6 kg bicycle moving with a velocity of 12 m/s?

Solution

Given data:

• Kinetic energy of a bicycle, KE = ?
• Mass of a bicycle, m = 6 kg
• Velocity of a bicycle, v = 12 m/s

Applying the formula:

• KE = ½ × m v2
• KE = ½ × 6 × (12)2
• KE = 3 × 144
• KE = 432 J

Therefore, the kinetic energy of a bicycle is 432 J.

Problem #3

Calculate the kinetic energy of an 800 kg car traveling at a velocity of 3 m/s.

Solution

Given data:

• Kinetic energy of a car, KE = ?
• Mass of a car, m = 800 kg
• Velocity of a car, v = 3 m/s

Applying the formula:

• KE = ½ × m v2
• KE = ½ × 800 × (3)2
• KE = 400 × 9
• KE = 3600 J

Therefore, the kinetic energy of a car is 3600 J.

Problem #4

A rail wagon weighing 400 kg has a velocity of 7 m/s. What is the kinetic energy of the rail wagon?

Solution

Given data:

• Mass of a rail wagon, m = 400 kg
• Velocity of a rail wagon, v = 7 m/s
• Kinetic energy of a rail wagon, KE = ?

Applying the formula:

• KE = ½ × m v2
• KE = ½ × 400 × (7)2
• KE = 200 × 49
• KE = 9800 J

Therefore, the kinetic energy of a rail wagon is 9800 J.